On the latency bound of pre-order deficit round robin

In the emerging high-speed packet-switched networks, packet scheduling algorithms used in the switches and routers will play a critical role in satisfying the quality of service (QoS) requirements of various applications. The latency bound of a scheduling discipline is an important QoS parameter, especially for real-time playback applications. Frame-based schedulers such as deficit round robin (DRR), though extremely efficient with an O(1) dequeuing complexity, lead to high latencies due to bursty transmissions of each flow´s traffic. In a previous work by, Tsao and Lin (see Computer Networks, vol.35, no.2-3, p.287-305, 2001), the authors propose pre-order deficit round robin, a novel scheme that overcomes this limitation of DRR while still achieving a low work complexity. In pre-order DRR, a priority queue module is appended to the original DRR scheduler which re-orders the packet transmission sequence in DRR to distribute the output more evenly among flows and thus reduce burstiness and improve the latency. We employ a novel approach to analytically derive the latency bound of pre-order DRR and show that our bound is a tight one. Our latency bound is significantly lower than the bound derived by Tsao and Lin, demonstrating that pre-order DRR has even better performance characteristics than previously argued by its own authors.